The invention relates to the display of piloting assistance information in an aircraft cockpit. Modern aircraft, in particular transport planes, include a system for displaying information in the cockpit thereof. Such a system, for example of CDS (“Control and Display System”) type commands the display of information on screens, called head-down screens, of the cockpit: to view this information, the user, generally a pilot or a co-pilot of the aircraft, must lower their head in order to look at the screens. They cannot therefore simultaneously see the environment of the aircraft through a windscreen of the cockpit. In order to allow the user to see a display of information without being forced to lower their head in order to look at the screens, some aircraft are now equipped with a head-up display (HUD) device or a display device configured to be worn such as to be rigidly connected to the head of the user. Such a device is commonly called a HMD meaning “head-mounted display.” It is sometimes also called a HWD meaning “head-worn display.” It generally includes a display mounted such as to be rigidly connected to glasses or to a headset, such that the user can see information displayed on the display when the user wears these glasses or this headset. In the remainder of the description, the term HMD refers to both a HMD device and a HWD device. The display is transparent such that the user can view the information displayed in a superimposed manner on the environment. In the whole description, the term transparent refers to both a completely transparent display and a semi-transparent (and consequently semi-reflective) display. The HUD or HMD devices thus allow the user to view information while looking at the external environment of the aircraft through a windscreen of the cockpit. Yet, when the user looks outside the aircraft through such a windscreen, the user can sometimes be dazzled by a light source external to the aircraft, such as the sun. In such a situation, it can be difficult for the user to read information displayed on the display device.